Couldn’t someone take out the drones pretty easily?

Helicopters aren't exactly robust under fire and are four orders of magnitude more valuable as a target.

That depends on the drone. There are drones/UAVs that fly so high in the air you can't even see them seeing you from the ground. Even low flying drones would be very hard to hit from a car involved in a high speed chase, and it's not as if people can't shoot at helicopters which are both larger/easier targets and much more dangerous if brought down.